TSTP Solution File: GRP430-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP430-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 00:20:15 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 6
% Syntax : Number of formulae : 62 ( 58 unt; 4 typ; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
inverse: $i > $i ).
tff(decl_23,type,
multiply: ( $i * $i ) > $i ).
tff(decl_24,type,
a1: $i ).
tff(decl_25,type,
b1: $i ).
cnf(single_axiom,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_1,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_1) ).
cnf(c_0_2,axiom,
multiply(X1,inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X1)))) = X4,
single_axiom ).
cnf(c_0_3,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X4))),multiply(X5,inverse(X5))),multiply(X3,X1)))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
multiply(X1,inverse(multiply(multiply(X2,multiply(X3,inverse(X3))),multiply(X4,X1)))) = multiply(multiply(multiply(X5,inverse(X5)),inverse(multiply(X2,X4))),multiply(X6,inverse(X6))),
inference(spm,[status(thm)],[c_0_2,c_0_3]) ).
cnf(c_0_5,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,multiply(X3,inverse(multiply(multiply(X4,multiply(X5,inverse(X5))),multiply(X2,X3))))))) = X4,
inference(spm,[status(thm)],[c_0_2,c_0_4]) ).
cnf(c_0_6,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,X3))) = multiply(multiply(X4,inverse(X4)),inverse(multiply(X2,X3))),
inference(spm,[status(thm)],[c_0_5,c_0_3]) ).
cnf(c_0_7,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_6]),c_0_2]) ).
cnf(c_0_8,plain,
multiply(X1,inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3)),X1)))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_9,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,multiply(multiply(multiply(X3,inverse(X3)),inverse(multiply(X4,X2))),X5))),multiply(multiply(multiply(X6,inverse(X6)),inverse(X4)),X1)))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_10,plain,
multiply(inverse(multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(X3,X1))),multiply(multiply(X4,inverse(X4)),inverse(multiply(X5,X6)))))),inverse(multiply(X6,X3))) = X5,
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_11,plain,
multiply(X1,multiply(multiply(multiply(X2,inverse(X2)),inverse(multiply(multiply(X3,inverse(X3)),X1))),X4)) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
multiply(X1,inverse(multiply(inverse(multiply(X2,X3)),multiply(multiply(multiply(X4,inverse(X4)),inverse(X5)),X1)))) = inverse(multiply(X6,multiply(multiply(multiply(X7,inverse(X7)),inverse(multiply(X3,X6))),multiply(multiply(X8,inverse(X8)),inverse(multiply(X5,X2)))))),
inference(spm,[status(thm)],[c_0_2,c_0_10]) ).
cnf(c_0_13,plain,
multiply(X1,inverse(multiply(multiply(multiply(multiply(X2,inverse(X2)),inverse(X3)),multiply(X4,inverse(X4))),multiply(X5,X1)))) = inverse(multiply(multiply(a1,inverse(multiply(multiply(X6,multiply(a1,inverse(a1))),multiply(X3,a1)))),multiply(X6,X5))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_3]),c_0_4]) ).
cnf(c_0_14,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(multiply(inverse(X2),multiply(X3,inverse(X3))))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_15,plain,
multiply(X1,inverse(multiply(inverse(multiply(multiply(a1,inverse(multiply(multiply(X2,multiply(a1,inverse(a1))),multiply(X3,a1)))),multiply(X2,X4))),multiply(multiply(multiply(X5,inverse(X5)),inverse(X3)),X1)))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_3]),c_0_4]) ).
cnf(c_0_16,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(multiply(X2,inverse(X2)),X3)) = X3,
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_17,plain,
multiply(multiply(a1,inverse(multiply(inverse(multiply(X1,X2)),multiply(multiply(multiply(a1,inverse(a1)),inverse(X3)),a1)))),inverse(multiply(X1,X2))) = X3,
inference(rw,[status(thm)],[c_0_10,c_0_12]) ).
cnf(c_0_18,plain,
inverse(multiply(multiply(a1,inverse(multiply(multiply(a1,multiply(a1,inverse(a1))),multiply(multiply(X1,X2),a1)))),multiply(a1,X1))) = X2,
inference(rw,[status(thm)],[c_0_3,c_0_13]) ).
cnf(c_0_19,plain,
multiply(multiply(a1,inverse(multiply(multiply(X1,multiply(a1,inverse(a1))),multiply(multiply(X2,inverse(X2)),a1)))),multiply(X1,X3)) = X3,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
multiply(inverse(multiply(X1,inverse(X1))),multiply(X2,inverse(X2))) = inverse(multiply(X3,inverse(X3))),
inference(spm,[status(thm)],[c_0_16,c_0_7]) ).
cnf(c_0_21,plain,
multiply(multiply(a1,inverse(multiply(X1,multiply(multiply(multiply(a1,inverse(a1)),inverse(X2)),a1)))),X1) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_22,plain,
multiply(multiply(a1,inverse(a1)),multiply(inverse(multiply(X1,inverse(X1))),X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]) ).
cnf(c_0_23,plain,
inverse(multiply(multiply(a1,inverse(multiply(multiply(a1,multiply(a1,inverse(a1))),X1))),multiply(a1,a1))) = inverse(multiply(a1,multiply(multiply(multiply(a1,inverse(a1)),inverse(X1)),a1))),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_24,plain,
multiply(multiply(X1,inverse(X1)),multiply(inverse(multiply(X2,inverse(X2))),X3)) = X3,
inference(spm,[status(thm)],[c_0_22,c_0_7]) ).
cnf(c_0_25,plain,
multiply(inverse(multiply(X1,inverse(X1))),inverse(inverse(multiply(X2,inverse(X2))))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_26,plain,
inverse(multiply(a1,multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(multiply(a1,X1),a1))),a1))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_27,plain,
multiply(X1,inverse(multiply(inverse(inverse(multiply(X2,inverse(X2)))),multiply(X3,X1)))) = inverse(X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_24]),c_0_19]) ).
cnf(c_0_28,plain,
multiply(multiply(a1,multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(multiply(a1,X1),a1))),a1)),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
cnf(c_0_29,plain,
inverse(multiply(inverse(X1),multiply(X2,inverse(X2)))) = multiply(multiply(a1,inverse(a1)),X1),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_30,plain,
multiply(multiply(a1,inverse(a1)),inverse(multiply(X1,inverse(X1)))) = multiply(X2,inverse(X2)),
inference(spm,[status(thm)],[c_0_22,c_0_20]) ).
cnf(c_0_31,plain,
multiply(X1,multiply(a1,inverse(a1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]),c_0_26]) ).
cnf(c_0_32,plain,
multiply(X1,multiply(X2,inverse(X2))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_7]) ).
cnf(c_0_33,plain,
multiply(multiply(a1,inverse(a1)),X1) = inverse(inverse(X1)),
inference(rw,[status(thm)],[c_0_29,c_0_32]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,inverse(X1)),inverse(multiply(X2,inverse(X2)))) = multiply(X3,inverse(X3)),
inference(spm,[status(thm)],[c_0_30,c_0_7]) ).
cnf(c_0_35,plain,
multiply(multiply(inverse(multiply(X1,inverse(X1))),X2),inverse(multiply(inverse(X3),X2))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_24]) ).
cnf(c_0_36,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_33]),c_0_32]),c_0_34]),c_0_33]) ).
cnf(c_0_37,plain,
inverse(inverse(inverse(multiply(a1,inverse(a1))))) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_34]) ).
cnf(c_0_38,plain,
multiply(multiply(a1,inverse(multiply(multiply(a1,multiply(a1,inverse(a1))),X1))),multiply(a1,a1)) = multiply(a1,multiply(multiply(multiply(a1,inverse(a1)),inverse(X1)),a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_35]) ).
cnf(c_0_39,plain,
inverse(multiply(a1,inverse(a1))) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(multiply(a1,a1),a1))),a1) = inverse(multiply(a1,multiply(multiply(a1,inverse(a1)),a1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_38]),c_0_7]) ).
cnf(c_0_41,plain,
multiply(multiply(X1,inverse(X1)),X2) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_33,c_0_7]) ).
cnf(c_0_42,plain,
inverse(multiply(X1,inverse(X1))) = multiply(X1,inverse(X1)),
inference(spm,[status(thm)],[c_0_39,c_0_7]) ).
cnf(c_0_43,plain,
inverse(multiply(a1,inverse(multiply(a1,multiply(multiply(a1,inverse(a1)),a1))))) = a1,
inference(spm,[status(thm)],[c_0_26,c_0_40]) ).
cnf(c_0_44,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_41]),c_0_42]),c_0_42]),c_0_42]),c_0_41]),c_0_41]),c_0_36]) ).
cnf(c_0_45,plain,
inverse(multiply(a1,inverse(multiply(a1,multiply(multiply(X1,inverse(X1)),a1))))) = a1,
inference(spm,[status(thm)],[c_0_43,c_0_7]) ).
cnf(c_0_46,plain,
inverse(inverse(X1)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_44]) ).
cnf(c_0_47,plain,
multiply(multiply(a1,inverse(multiply(a1,multiply(multiply(X1,inverse(X1)),a1)))),a1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_45]),c_0_25]) ).
cnf(c_0_48,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(rw,[status(thm)],[c_0_41,c_0_46]) ).
cnf(c_0_49,plain,
multiply(a1,inverse(multiply(a1,a1))) = inverse(a1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_45]),c_0_41]),c_0_46]) ).
cnf(c_0_50,plain,
multiply(a1,multiply(a1,inverse(a1))) = a1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_47]),c_0_29]),c_0_34]),c_0_45]) ).
cnf(c_0_51,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
prove_these_axioms_1 ).
cnf(c_0_52,plain,
multiply(inverse(a1),a1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42]),c_0_41]),c_0_46]),c_0_49]) ).
cnf(c_0_53,plain,
multiply(X1,multiply(inverse(X2),X2)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_46]) ).
cnf(c_0_54,plain,
inverse(multiply(a1,multiply(multiply(multiply(a1,inverse(a1)),inverse(multiply(a1,a1))),a1))) = multiply(a1,inverse(a1)),
inference(spm,[status(thm)],[c_0_26,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
multiply(inverse(b1),b1) != multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
multiply(inverse(X1),X1) = multiply(a1,inverse(a1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_53]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP430-1 : TPTP v8.1.2. Released v2.6.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:09:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.75 % Version : CSE_E---1.5
% 0.19/0.75 % Problem : theBenchmark.p
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark.p
% 0.19/0.75 % SZS output start Proof
% See solution above
% 0.19/0.76 % Total time : 0.175000 s
% 0.19/0.76 % SZS output end Proof
% 0.19/0.76 % Total time : 0.178000 s
%------------------------------------------------------------------------------